Cook Pasta
Bring a large pot of salted water to a boil. Cook pasta until al dente. Reserve ½ cup pasta water, then drain.
Cook Broccoli
Add broccoli to the boiling pasta water during the last 2–3 minutes of cooking, or steam separately until tender-crisp.
Sauté Garlic
Heat olive oil in a large skillet over medium heat. Add garlic and cook 30–60 seconds until fragrant (do not brown).
Combine
Add pasta and broccoli to the skillet. Toss gently to coat.
Finish Sauce
Add reserved pasta water a little at a time to create a light sauce. Season with salt, pepper, and red pepper flakes if using.
Add Cheese & Serve
Remove from heat and stir in grated cheese. Serve warm.